The Diophantine equation given by ax^2 + by^2 + cz^2 = 0 is named for this mathematician who conject
The Diophantine equation given by ax^2 + by^2 + cz^2 = 0 is named for this mathematician who conjectured that there is a prime number between n^2 and (n+1)^2 for every integer n and proved that pi squared is irrational. The Dirichlet ["dee-ree-klay"] character generalizes this man's "symbol," which for an integer a and a prime p returns either 1, -1, or 0, depending on whether or not a is a quadratic residue mod p. His transformation, which is generalized by convex conjugation and is denoted (*) f-star, satisfies the functional equation "f-star of f-prime of x equals x times f-prime of x minus f of x." His namesake differential equation is encountered when solving the Laplace equation in spherical coordinates. For 10 points, name this French mathematician perhaps best known for an eponymous set of polynomials used in calculating spherical harmonics.
The Diophantine equation given by ax^2 + by^2 + cz^2 = 0 is named for this mathematician who conjectured that there is a prime number between n^2 and (n+1)^2 for every integer n and proved that pi squared is irrational.
Adrien-Marie {Legendre}